WO 2011/067265 A1 describes a phase modulator for modulating light interacting with the phase modulator. The phase modulator described in WO 2011/067265 A1 for modulating the phase of circularly polarized light contains inter alia a first and a second substrate and a liquid crystal layer between the two substrates, the surfaces of the substrates being configured in order to orientate the liquid crystal molecules next to the first surface in a direction which is substantially parallel to the first surface, and to orientate the liquid crystal molecules next to the second surface in a direction which is substantially perpendicular to the second surface. Such an orientation is also referred to as hybrid alignment of a nematic (HAN) liquid crystal.
As disclosed by WO 2011/067265 A1, such a HAN configuration is used in order selectively to achieve a rotation of the in-plane component of the liquid crystal molecule orientation, for example from 0 to +90 degrees or from 0 to −90 degrees, as a function of the sign of the electric field applied to the electrodes, and therefore to achieve overall a phase modulation of from 0 to 2π by such control of the applied field. The thickness of the LC layer is in this case preferably selected in such a way that its optical function corresponds to a λ/2 plate.
The sign-dependent rotation in the electric field is in this case based on flexoelectric polarization. This polarization is based on a mechanical deformation of the LC, or the LC molecules, by the hybrid alignment.
WO 2011/067265 A1 also describes such a phase modulator, which is configured in such a way that the light interacting with the phase modulator can be variably deviated as a result of diffraction in a predeterminable direction, and that the function of a variably adjustable deflection grating can thereby be achieved.
A variable deflection grating based on phase modulation, used in a manner comparable to that described in DE 10 2009 028 626 A1, may be produced by individual driving of individual in-plane electrodes.
Because of the hybrid alignment, the LC molecules are partially oriented out-of-plane, specifically as an average value over the layer thickness approximately at 45 degrees, with a linear variation between approximately 0 and 90 degrees from one surface of the liquid crystal layer to the other.
The effective birefringence for light which passes through an LC layer, the LC molecules being tilted at an angle β with respect to the direction in which the light passes through, is
      Δ    ⁢                  ⁢          n      eff        =            n      2        -                            n          1                ·                  n          2                                                                                n                1                2                            ·                              sin                2                                      ⁢            β                    +                                                    n                2                2                            ·                              cos                2                                      ⁢            β                              
where n1 and n2 are the ordinary and extraordinary refractive indices of the liquid crystal with the birefringence Δn=n2−n1.
For a hybrid alignment, the angle β varies over the layer thickness between 0 and 90 degrees, and Δneff consequently also varies over the thickness of the LC layer. The effective optical path difference (opd), which in the case of uniform LC orientation is usually described as opd=d Δn with the layer thickness d and the birefringence Δn, is in this caseopd=∫0dΔneff(z)dz 
For hybrid orientation, an average effective birefringence over the layer thickness is approximately Δneff≈0.5 Δn
and the optical path difference is opdHAN≈0.5 d Δn.
The effective optical path difference for light passing perpendicularly through the liquid crystal layer is less than the case would be with a liquid crystal layer in which the liquid crystal molecules are oriented in-plane. In order to achieve the optical function of a λ/2 plate, the product of the layer thickness of the LC layer and the birefringence of the LC material must therefore be relatively large. In the case of a layer thickness of 3 micrometers, approximately a Δn of 0.18 is required in order to adjust a λ/2 plate for green light. Specifically, with these numerical values opdHAN≈0.5·0.18·3 μm=0.27 μm, which corresponds approximately to half the value of the wavelength of green light.
Usually, it is difficult to achieve this birefringence of 0.18 or a similar value as a material property in combination with, at the same time, a low viscosity. The use of an LC material with increased viscosity, however, compromises the maximum adjustable adjustment speed of the variably adjustable phase modulator.
The sign-dependent rotation of the liquid crystal molecules in the electrical in-plane field is based on flexoelectric polarization. The interaction of the polarization with the field is linear. Besides flexoelectric polarization, a quadratic interaction of the dielectric anisotropy Δε with the field also takes place.
In particular, the dielectric interaction may have the effect that, with higher fields, besides the desired rotation of the in-plane component of the LC molecule orientation an undesired rotation, coupled therewith, of the out-of-plane component of the LC molecule orientation also takes place in the field. This rotation of the out-of-plane component of the LC molecule orientation has the effect that the LC layer no longer fulfills the optical function of a λ/2 plate. In the worst case, the optical path through the LC layer may be doubled. This is because if all the LC molecules are oriented in-plane, i.e. parallel to the substrates, the optical path would be opdparallel=d Δn=2·opdHAN.
A change in the optical path with the in-plane rotation angle leads, particularly when using the phase modulator as a variable deflection grating, to a reduced diffraction efficiency of the deflection grating. Less light thus enters the desired diffraction order, and under certain circumstances undesired perturbing light enters other diffraction orders.
Correct functioning of the HAN phase modulator as a variable deflection grating therefore requires a liquid crystal material with a high flexoelectric coefficient and, at the same time, a low dielectric anisotropy Δε. Preferably, Δε lies in the range of less than 2, ideally less than 0.2. As described above, this is required in combination with a high birefringence Δn of the liquid crystal material, preferably in the range of from 0.15 to 0.2.
It would be desirable to have a phase modulator which can also be used as a variable deflection grating, which avoids the described disadvantages and which in particular makes it possible to use liquid crystal materials whose material parameters lie closer to standard values of currently used materials.
For example, the birefringence Δn of liquid crystal materials used at present in displays typically lies in the range of from 0.8 to 0.10 and the dielectric anisotropy Δε typically lies in the range of from 5 to 10.
U.S. Pat. No. 7,564,510 B2 describes a liquid crystal display device which contains pixels, each pixel being subdivided into a number of regions, and the direction of an electric field—substantially parallel to the substrates—in one of the regions being opposite to the field direction in another region, and in the case of which there is furthermore a polarization in the liquid crystal layer when no field is applied. U.S. Pat. No. 7,564,510 B2 therefore describes a pixel structure which generates a uniform brightness impression for large observer angle in that different regions of a pixel compensate for one another in the overall brightness of the pixel for different viewing directions. For example, when observed from one particular direction, a first region of the pixel appears brighter and a second region appears darker. Observed from another direction, the situation is reversed. Yet since the eye cannot resolve the regions of the pixel individually, there is a uniform brightness impression.
To this end, in U.S. Pat. No. 7,564,510 B2, a rotation of the liquid crystal molecule orientation as a function of the sign of the electric field is used so that the liquid crystal molecules in different regions of a pixel thus rotate oppositely. It is described that this sign-dependent rotation may likewise be based on flexoelectric polarization.
FIG. 3 of U.S. Pat. No. 7,564,510 B2 describes a configuration with parallel rubbing on the two surfaces of the substrates. This leads to a mirror-symmetrically equal alignment of the LC molecules on the two substrates (with a mirror plane parallel to the substrates in the middle of the LC layer) and a splay deformation in the LC layer between the two substrates. This splay deformation generates flexoelectric polarization.
The arrangement described in U.S. Pat. No. 7,564,510 B2 would not, however, be usable as a phase modulator since the different regions of a pixel would respectively generate different phase values, so that a full pixel would not have uniform phase modulation.